A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34,25 Inches (in.), a height of 69,37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping box?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
Other Related Questions
For an emergency service call, a plumbing company charges a flat fee of $60 plus $40 an hour. A customer remembers paying at least $200 for an emergency service. Which phrase describes the number of hours the plumbing company was at the service call?
- A. at most 2 hours
- B. at most 3.5 hours
- C. at least 3.5 hours
- D. at least 2 hours
Correct Answer & Rationale
Correct Answer: C
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 ÷ $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 ÷ $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
A cyclist can travel 17.6 feet per second. The cyclist would have a better understanding of her speed if it were measured in miles per hour. Which of these completes the expression used to convert the speed of the cyclist to miles per hour?
- A. 1 hour/60 seconds = 1 mile/5,280 feet
- B. 60 minutes/1 hour = 1 mile/5280 feet
- C. 60 minutes/1 hour = 5280 feet/1 mile
- D. 12 inches/1 foot = 60 minutes/1 hour
Correct Answer & Rationale
Correct Answer: C
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
The world's highest suspension bridge spans the Arkansas River at a height of 1,053 feet above the water. If a ball is dropped from the bridge. The height of the ball, In feet, after t seconds can be modeled by the equation f(t)= -16(t)^2 + 1053. How many feet above the water is the ball 7 seconds after being dropped?
Correct Answer & Rationale
Correct Answer: A
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
The daily cost, C(x), tor a company to produce x microscopes is given by the equation C(x) = 300 + 10.5x. What is the cost of producing 50 microscopes?
- A. $41,250
- B. $360.50
- C. $15,525
- D. $825
Correct Answer & Rationale
Correct Answer: D
To find the cost of producing 50 microscopes, substitute x = 50 into the cost equation C(x) = 300 + 10.5x. This yields C(50) = 300 + 10.5(50), resulting in C(50) = 300 + 525 = 825. Thus, the cost for 50 microscopes is $825. Option A ($41,250) is incorrect as it likely results from a miscalculation or misunderstanding of the equation. Option B ($360.50) underestimates the production cost by omitting the correct multiplication factor. Option C ($15,525) suggests an error in the calculation, possibly misinterpreting the coefficients in the equation.
To find the cost of producing 50 microscopes, substitute x = 50 into the cost equation C(x) = 300 + 10.5x. This yields C(50) = 300 + 10.5(50), resulting in C(50) = 300 + 525 = 825. Thus, the cost for 50 microscopes is $825. Option A ($41,250) is incorrect as it likely results from a miscalculation or misunderstanding of the equation. Option B ($360.50) underestimates the production cost by omitting the correct multiplication factor. Option C ($15,525) suggests an error in the calculation, possibly misinterpreting the coefficients in the equation.